Compression- The region of a longitudinal wave in which the density and pressure are greater than normal
Rarefaction- The region of a longitudinal wave in which the density and pressure are less than normal
Sound waves are longitudinal
Characteristics of Sound Waves
Sound waves that the average human ear can hear are called audible sound waves.
They have frequencies between 20 and 20 000 Hz.
Sound waves with frequenices less than 20 Hz are called infrasonic waves.
Those above 20 000 Hz are called ultrasonic waves.
Frequency determines pitch.
Pitch- The perceived highness or low-ness of a sound, depending on the frequency of the sound waves.
Ultrasonic waves can produce images.
Speed of sound depends on the medium.
Sound waves propagate in three dimensions.
The circles that represent the centers of compression are called wave fronts.
The radial lines perpendicular to the wave fronts are called rays.
Any small portion of a spherical wave that is far from the source can be considered a plane wave.
The Doppler Effect
Relative motion creates a change in frequency.
Doppler effect- A frequency shift that is the result of relative motion between the source of waves and an observer.
The Doppler effect occurs whenever there is relative motion between the source of waves and an observer.
13-2: Sound Intensity and Resonance
Sound Intensity
Intensity is the rate of energy flow through a given area.
Intensity- The rate at which energy flows through a unit area perpendicular to the direction of wave motion.
Because power, P, is deined as the rate of energy transfer, intensity can also be described in terms of power.
The SI unit for power is the watt, thus intensity has units of watts per square meter (W/m²).
Internsity of a spherical wave.
Intensity= (P/4πr²)
Intensity and frequency determine which sounds are audible.
Threshold of hearing- The softest sounds that can be heard by the average human ear occur at a frequency of about 1000 Hz and an intensity of 1.0 X 10¯¹² W/m².
Threshold of pain- The loudest sounds that the human ear can tolerate have an intensity of about 1.0 W/m².
Relative intensity is measure in decibles.
Decibel level- Relative intensity, determined by relating the intensity of a sound wave to the intensity at the threshold of hearing.
Forced Vibrations and Resonance
Vibration at the natural frequency produces resonance.
Resonance- A condition that exists when the frequency of a force applied to a system matches the natural frequency of vibration of the system.
The human ear transmits vibrations that cause nerve impluses.
13:3 Harmonic
Standing Waves On a Vibrating String
Fundamental frequency- The lowest frequency of vibration of a standing wave.
Harmonics are integral multiples of the fundamental frequency.
Harmonic series- A series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency.
Harmonic series of standing waves on a vibrating string:
Fn=n(V/2L) n= 1,2,3,...
Standing waves in an air column
If both ends of a pipe are open, all harmonics are present
Harmonic series of a pipe open at both ends:
Fn=n(V/2L) n= 1,2,3,...
If one end of a pipe is closed, only odd harmonics are present
Harmonic series of a pipe closed at one end:
Fn=n(V/4L) n= 1,3,5,...
Harmonics account for sound quality, or timbre.
Timbre- The quality of a steady musical sound that is the result of a mixture of harmonics present at different intensities.
Notes that each consist of repeating patterns are said to be periodic.
Fundamental frequency determines pitch.
The frequency of the thirteenth note is exactly twice that of the first note, and togeather the 13 notes constitute an octave.
Beats
When two waves of slightly different frequencies interfere, the interference pattern varies in such way that a listener hears an alternation between loudness and softness.
Beat- Interference of waves of slightly different frequencies traveling in the same direction, perceived as a variation in loudness.
Sound waves at slightly different frequencies produce beats.
When the two waves are exactly opposite one another, they are said to be out of phase.
The number of beats per second corresponds to the difference between frequencies.
The expansion of the universe.
The eruption of the universe is often referred to as the big bang.
Experimental verification.
Practice Problems:
1) Calculate the intensity of the sound waves from an electric guitar's amplifier at a distance of 5.0m when its power output is equal to each of the following values:
a. 0.25 W
b. 0.50 W
c. 2.0 W
2) If the intensity of a person's voice is 4.6 X 10^ -7 W/m² at a distance of 2.0 m, how much sound power deos that person generate?
3) The power output of a tuba is 0.35 W. At what distance is the sound intensity of the tube 1.2 X 10^ -3 W/m²?
4) What is the fundamental frequency of a 0.20 m long organ pipe that is closed at one end, when the speed of sound in the pipe is 352 m/s?
5) What is the fundamental frequency of a guitar string when the speed of waves on the string is 115 m/s and the effective string lengths are as follows:
a. 70.0 cm
b. 50.0 cm
c. 40.0 cm
Answers:
1. a. 8.0 X 10^ -4 W/m², b. 1.6 X 10^ -3 W/m², c. 6.4 X 10^ -3 W/m²
2. 2.3 X 10^ -5 W
3. 4.8 m
4. 440 Hz
5. a. 82.1 Hz, b. 115 Hz, c. 144 Hz
Holt, Rinehart and Holt Physics. New York: Holt, Rinehart & Winston, 2001.
13-1: Sound Waves
The Production of Sound Waves
Characteristics of Sound Waves
The Doppler Effect
13-2: Sound Intensity and Resonance
Sound Intensity
Forced Vibrations and Resonance
13:3 Harmonic
Standing Waves On a Vibrating String
- Fundamental frequency- The lowest frequency of vibration of a standing wave.
- Harmonics are integral multiples of the fundamental frequency.
- Harmonic series- A series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency.
- Harmonic series of standing waves on a vibrating string:
- Fn=n(V/2L) n= 1,2,3,...
Standing waves in an air columnBeats
Practice Problems:
1) Calculate the intensity of the sound waves from an electric guitar's amplifier at a distance of 5.0m when its power output is equal to each of the following values:
a. 0.25 W
b. 0.50 W
c. 2.0 W
2) If the intensity of a person's voice is 4.6 X 10^ -7 W/m² at a distance of 2.0 m, how much sound power deos that person generate?
3) The power output of a tuba is 0.35 W. At what distance is the sound intensity of the tube 1.2 X 10^ -3 W/m²?
4) What is the fundamental frequency of a 0.20 m long organ pipe that is closed at one end, when the speed of sound in the pipe is 352 m/s?
5) What is the fundamental frequency of a guitar string when the speed of waves on the string is 115 m/s and the effective string lengths are as follows:
a. 70.0 cm
b. 50.0 cm
c. 40.0 cm
Answers:
1. a. 8.0 X 10^ -4 W/m², b. 1.6 X 10^ -3 W/m², c. 6.4 X 10^ -3 W/m²
2. 2.3 X 10^ -5 W
3. 4.8 m
4. 440 Hz
5. a. 82.1 Hz, b. 115 Hz, c. 144 Hz
Holt, Rinehart and Holt Physics. New York: Holt, Rinehart & Winston, 2001.